A method has been proposed for obtaining confidence intervals for the differences between treatment means in an analysis of variance. The intervals have the following properties: (1) The probability that the interval will cover the parameter is greater than or equal to (1 - α), and (2) If the same procedure is applied simultaneously to each of the pO2 differences among p means, the probability that all confidence intervals will cover the parameters correctly is at least (1 - α) ^{p - 1}. The same properties hold if the procedure is simultaneously applied to special linear comparisons among the means as well as to differences between single means. The intervals are complex in that the limits are dependent on the values of nuisance parameters. Three alternatives for handling these nuisance parameters are discussed, and one is preferred for use in practice. / Master of Science